... ON THE ESTIMATION OF UPPER BOUND FOR SOLUTIONS
OF PERTURBED DISCRETE LYAPUNOV EQUATIONS
DONG-YAN CHEN AND DE-YU WANG
Received 20 February 2006; Revised 4 June 2006; Accepted 12 June 2006
The estimation ... definite solutions P to (1.1)
and P<
X.Theproofiscompleted.
Remark 2.9. From the relations between the solution of the perturbed discrete Lyapun...
... to the
length of as-obtained nanowire. However, when the
thickness is rather high (etc. lm order), the film is unlikely
to melt into molten droplets within the thermal treatment.
Therefore, the ... obvious; but both of the others
show a good line with almost the same slope. The fol-
lowing are the reasons for the nonlinearity. First, from the
corresponding SEM image...
... features of the
cover image. The pinned field [19-22] reflects the t ex-
ture information of the cover image by evaluating the
average pixel values at block boundaries of the image
and is used as the ... pixel values at block boundaries
of the images and can be used as the feature of the
cover image to enhance the watermark robustness. The
reasons of choosi...
... importantly, superiority of one
type of therapy over another could not be distinguished,
and therefore that the specific choice of therapy was diffi-
cult to justify over another type of treatment. This ... the benefit of various
types of physical therapies.
Evolution of physical rehabilitation
Historically, the management of stroke survivors involved
bed-rest and conval...
... values for
the different parameters of the classification algorithm,
the ability of discriminating the different stimuli was
investigated. In particular, the median and the maximum
of the classification ... means of
implanted interfaces with the peripheral nerves of the
subject [12]. In the latter case, the choice of the electrode
will make a difference o...
...
processes encapsulate the synapse and cover also the ablumi-
nal side of the blood vessel wall (right). The endothelial cells
covering the luminal (blood) side of the vessel wall and the
astrocytic ... its cause and
the prognosis, is of utmost importance for breaking the
vicious circle, which comes with the risk for secondary
anxiety and depression. Furthermor...
... also the mucous membranes of the
throat."
Then they mixed all the "stuff" together and sprayed 1 cc
of the mixture in each of the nostrils of 10 volunteers, and
"into the throat, ... was the largest of the studies, illustrative
of the attempts, and remarkable for the courageousness of
the volunteers [52]. In 1919 – in a series of exp...
... that
m
k
n
<
|
a
n
|
.
3. Proof of the theorem
Proof of Theorem 1.1.Letm =min
|z|=k
|p(z)|. If p( z)hasazeroon|z|=k,thenm =
0 and the result follows from Lemma 2.8. Henceforth, we suppose that all the zeros of
p(z) ... contradicts the fact that |a
1
|>k. Hence, the polynomial
D
α
1
p(z)
must
be of degree (n - 1).
On the other hand, since all the zeros of p(z) lie...
... type, the proof is clear.
In the followin g theorem, we generalize the well-known Baker’s super-stability result
for e xponential mappings with values in the field of complex numbers to the case of
an ... satisfies the inequality
||f (x ∗ y) − f(x) ∗ f(y)||
H
≤ α
for some a ≥ 0 and for all x; y Î G, then f(x * y)=f(x)*f(y) for all x; y Î G.
In the next theorem, we ge...
... f(x)
≤
1
4
n+1
k=1
2
r
2k
ϕ
r
2
k
x,
r
2
k
x
for all x Î X. Hence inequality (3.4) holds for all n Î N.
The proof of the case |r| < 2 is similar to the above proof. □
In the following theorem we find that for some conditions there ... School of Education,
Kyung Hee University, Yongin 446-
701, Republic of Korea
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